Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.
Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.
Folding operation 1 is carried out on Sheet M three times.
Folding operation 2 is carried out on Sheet N three times.
The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ________.
Sheet M Perimeter Calculation
Initial dimensions: Sheet M starts as a 6 cm x 4 cm rectangle.
Folding Operation 1: This operation involves folding the sheet by joining the short edges. With dimensions $L \times W$ where $L \ge W$, the short edges have length $W$. Joining them means the fold is parallel to the long edge ($L$), and the long dimension ($L$) is halved.
- Fold 1: Initial dimensions are 6 cm x 4 cm. Joining the 4 cm edges halves the 6 cm dimension. New dimensions: 3 cm x 4 cm.
- Fold 2: Current dimensions are 3 cm x 4 cm. The longer dimension is 4 cm, shorter is 3 cm. Joining the short (3 cm) edges halves the 4 cm dimension. New dimensions: 3 cm x 2 cm.
- Fold 3: Current dimensions are 3 cm x 2 cm. The longer dimension is 3 cm, shorter is 2 cm. Joining the short (2 cm) edges halves the 3 cm dimension. New dimensions: 1.5 cm x 2 cm.
Final Dimensions (Sheet M): 1.5 cm x 2 cm.
Perimeter Calculation (Sheet M): The perimeter $P_M$ is calculated using the formula $P = 2 \times (length + width)$. $P_M = 2 \times (1.5 \text{ cm} + 2 \text{ cm}) = 2 \times 3.5 \text{ cm} = 7 \text{ cm}$.
Sheet N Perimeter Calculation
Initial dimensions: Sheet N also starts as a 6 cm x 4 cm rectangle.
Folding Operation 2: This operation involves folding the sheet by joining the long edges. With dimensions $L \times W$ where $L \ge W$, the long edges have length $L$. Joining them means the fold is parallel to the short edge ($W$), and the short dimension ($W$) is halved.
- Fold 1: Initial dimensions are 6 cm x 4 cm. Joining the 6 cm edges halves the 4 cm dimension. New dimensions: 6 cm x 2 cm.
- Fold 2: Current dimensions are 6 cm x 2 cm. The longer dimension is 6 cm, shorter is 2 cm. Joining the long (6 cm) edges halves the 2 cm dimension. New dimensions: 6 cm x 1 cm.
- Fold 3: Current dimensions are 6 cm x 1 cm. The longer dimension is 6 cm, shorter is 1 cm. Joining the long (6 cm) edges halves the 1 cm dimension. New dimensions: 6 cm x 0.5 cm.
Final Dimensions (Sheet N): 6 cm x 0.5 cm.
Perimeter Calculation (Sheet N): The perimeter $P_N$ is calculated as follows: $P_N = 2 \times (6 \text{ cm} + 0.5 \text{ cm}) = 2 \times 6.5 \text{ cm} = 13 \text{ cm}$.
Ratio of Perimeters
The question asks for the ratio of the perimeter of the final folded shape of Sheet N to Sheet M ($P_N : P_M$).
Ratio Calculation: $\frac{P_N}{P_M} = \frac{13 \text{ cm}}{7 \text{ cm}} = \frac{13}{7}$
The ratio is 13:7.
Important Questions from Paper Folding
The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube?
Note: The figures shown are representative.
A planar rectangular paper has two V-shaped pieces attached as shown below.
This piece of paper is folded to make the following closed three-dimensional object.
The number of folds required to form the above object is
Consider a cube made by folding a single sheet of paper of appropriate shape.
The interior faces of the cube are all blank. However, the exterior faces that arenot visible in the above view may not be blank.
Which one of the following represents a possible unfolding of the cube?Two identical sheets A and B, of dimensions $24$ cm $\times$ $16$ cm, can be folded into half using two distinct operations, FO1 or FO2.
In FO1, the axis of folding remains parallel to the initial long edge, and in FO2, the axis of folding remains parallel to the initial short edge.
If sheet A is folded twice using FO1, and sheet B is folded twice using FO2, the ratio of the perimeters of the final shapes of A and B is
A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________________.
